Non-planarity in four-membered homo-cyclic compounds A₄ (A = O, S, Se, Te, Po) and restoring their planarity: a study of the pseudo-Jahn–Teller effect

Abstract

The bent D_2d structures of the four-membered homo-cyclic compounds A₄ (A = O, S, Se, Te, Po) were examined computationally to understand the pseudo-Jahn–Teller effect (PJTE). To do this, ab initio geometry optimizations and corresponding frequency calculations (at the MP2/cc-pVQZ-(PP) level of theory) show that all A₄ compounds under-consideration are unstable in their planar (D_4h) configuration. The ground state and six low-lying non-degenerate and degenerate electronic excited states were computed at the CASSCF (6,7)/cc-pVQZ-(PP) along the bending normal coordinate connecting the D_4h and D_2d geometries; these represent the adiabatic potential energy surfaces (APESs). Based on the APESs, the coupling between the ground state (¹A_1g) and the ¹B_2u excited state is demonstrated to be the reason for the planar structure bends from the high-symmetry D_4h geometry into the lower-symmetry D_2d stable equilibrium configuration. The solution to the PJTE (¹A_1g + ¹B_2u) ⊗ b_2u problem is useful to answer the question of “how instability rises in A₄ planar configuration?”. Although all A₄ compounds in the series are non-planar with D_4h symmetry, but geometrical optimizations and frequency calculations show that coordination of two noble gas cations (NG⁺ = He⁺, Ne⁺ and Ar⁺) above and below the σ_h plane of the A₄ (A = O, S, Se) ring could restore ring planarity in (A₄ NG)²⁺ complexes. The PJTE is also quenched in the A₄²⁺ (A = O, S, Se, Te, Po) cation and dication series, and planarity of the rings is also restored, i.e., the high-symmetry D_4h structure becomes the equilibrium configuration.